Page 891 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

and

(a) Use the cofactor expansion of determinants to show that
for , 4, 5, …. This says, for example, that

and so on. Using a computer, check this result for .
(b) By writing

and the identity, , in matrix form,

show that

(c) Use the methods in Section 7.2 and a computer to show that

and hence

for , 2, 3, …. .
(d) Using a computer, check this result for

In this exercise, we determine a formula for calculating from for , 1, 2, 3, …, n, assuming that is defined t
T2. be 1.

(a) Use a computer to compute for , 2, 3, 4, and 5.

(b) From your results in part (a), discover the conjecture that